Question 1: The profit maximization problem of the firm in the two-period model with investment is where and max V = 7+ N, N', I π' 1+r π = 2K NB-WN - I T' = 2'K'N'B -w'N' + (1 - d)K' K' = (1-d)K+I Parameters a and 3 are both positive and sum up to less than 1, i.e. a>0, ß>0, and (a + B) < 1. 1. Solve the first-order conditions for the firm's optimization problem and derive algebraic expressions for optimal N, N' and I. 1 2. The elasticity of labour demand is defined as N = ON w ὃω Ν Use the expression for optimal labour demand from part (1) to derive an expression for N. What is the range for nN? If ß = 1/3, what is nN? Interpret your answer.
Question 1: The profit maximization problem of the firm in the two-period model with investment is where and max V = 7+ N, N', I π' 1+r π = 2K NB-WN - I T' = 2'K'N'B -w'N' + (1 - d)K' K' = (1-d)K+I Parameters a and 3 are both positive and sum up to less than 1, i.e. a>0, ß>0, and (a + B) < 1. 1. Solve the first-order conditions for the firm's optimization problem and derive algebraic expressions for optimal N, N' and I. 1 2. The elasticity of labour demand is defined as N = ON w ὃω Ν Use the expression for optimal labour demand from part (1) to derive an expression for N. What is the range for nN? If ß = 1/3, what is nN? Interpret your answer.
Chapter1: Making Economics Decisions
Section: Chapter Questions
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Transcribed Image Text:Question 1: The profit maximization problem of the firm in the two-period model with
investment is
where
and
max V = 7+
N, N', I
T = 2K N³wN-I
π = 2K'N'B -w'N' + (1 - d)K'
π'
1+r
K' = (1-d) K+I
Parameters a and 3 are both positive and sum up to less than 1, i.e. a>0, ß>0, and
(a + B) < 1.
1. Solve the first-order conditions for the firm's optimization problem and derive algebraic
expressions for optimal N, N' and I.
1
2. The elasticity of labour demand is defined as
nN=
ON w
θω Ν
Use the expression for optimal labour demand from part (1) to derive an expression
for N. What is the range for n? If ß = 1/3, what is nN? Interpret your answer.
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Step 1: To solve the profit maximization problem in the two-period model with investment:
VIEWStep 2: Calculate the first-order derivatives of the Lagrangian function with respect to N, N' and I:
VIEWStep 3: 2. Formulate the expression for the elasticity of labor demand:
VIEWStep 4: Range of the Elasticity of Labor Demands:
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